Multiple liquid bridges with non-smooth interfaces
We consider a coexistence of two axisymmetric liquid bridges LB i and LB m of two immiscible liquids i and m which are immersed in a third liquid (or gas) e and trapped between two smooth solid bodies with axisymmetric surfaces S 1 , S 2 and free contact lines. Evolution of liquid bridges allows two...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Physik 2016-08, Vol.67 (4), p.1-13, Article 107 |
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| container_title | Zeitschrift für angewandte Mathematik und Physik |
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| creator | Fel, Leonid G. Rubinstein, Boris Y. Ratner, Vadim |
| description | We consider a coexistence of two axisymmetric liquid bridges LB
i
and LB
m
of two immiscible liquids
i
and
m
which are immersed in a third liquid (or gas)
e
and trapped between two smooth solid bodies with axisymmetric surfaces
S
1
,
S
2
and free contact lines. Evolution of liquid bridges allows two different configurations of LB
i
and LB
m
with multiple (five or three) interfaces of non-smooth shape. We formulate a variational problem with volume constraints and present its governing equations supplemented by boundary conditions. We find a universal relationship between curvature of the interfaces and discuss the Neumann triangle relations at the singular curve where all liquids meet together. |
| doi_str_mv | 10.1007/s00033-016-0702-7 |
| format | Article |
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i
and LB
m
of two immiscible liquids
i
and
m
which are immersed in a third liquid (or gas)
e
and trapped between two smooth solid bodies with axisymmetric surfaces
S
1
,
S
2
and free contact lines. Evolution of liquid bridges allows two different configurations of LB
i
and LB
m
with multiple (five or three) interfaces of non-smooth shape. We formulate a variational problem with volume constraints and present its governing equations supplemented by boundary conditions. We find a universal relationship between curvature of the interfaces and discuss the Neumann triangle relations at the singular curve where all liquids meet together.</description><identifier>ISSN: 0044-2275</identifier><identifier>EISSN: 1420-9039</identifier><identifier>DOI: 10.1007/s00033-016-0702-7</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of mathematics ; Axisymmetric ; Axisymmetric bodies ; Boundary conditions ; Contact ; Engineering ; Evolution ; Liquid bridges ; Liquids ; Mathematical analysis ; Mathematical Methods in Physics ; Theoretical and Applied Mechanics ; Triangles</subject><ispartof>Zeitschrift für angewandte Mathematik und Physik, 2016-08, Vol.67 (4), p.1-13, Article 107</ispartof><rights>Springer International Publishing 2016</rights><rights>Copyright Springer Science & Business Media 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c301t-dfd364be8ba3dc8723885009a2a575c23c912b01600172f3c0f35b1e55686f9e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00033-016-0702-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00033-016-0702-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Fel, Leonid G.</creatorcontrib><creatorcontrib>Rubinstein, Boris Y.</creatorcontrib><creatorcontrib>Ratner, Vadim</creatorcontrib><title>Multiple liquid bridges with non-smooth interfaces</title><title>Zeitschrift für angewandte Mathematik und Physik</title><addtitle>Z. Angew. Math. Phys</addtitle><description>We consider a coexistence of two axisymmetric liquid bridges LB
i
and LB
m
of two immiscible liquids
i
and
m
which are immersed in a third liquid (or gas)
e
and trapped between two smooth solid bodies with axisymmetric surfaces
S
1
,
S
2
and free contact lines. Evolution of liquid bridges allows two different configurations of LB
i
and LB
m
with multiple (five or three) interfaces of non-smooth shape. We formulate a variational problem with volume constraints and present its governing equations supplemented by boundary conditions. We find a universal relationship between curvature of the interfaces and discuss the Neumann triangle relations at the singular curve where all liquids meet together.</description><subject>Applications of mathematics</subject><subject>Axisymmetric</subject><subject>Axisymmetric bodies</subject><subject>Boundary conditions</subject><subject>Contact</subject><subject>Engineering</subject><subject>Evolution</subject><subject>Liquid bridges</subject><subject>Liquids</subject><subject>Mathematical analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Theoretical and Applied Mechanics</subject><subject>Triangles</subject><issn>0044-2275</issn><issn>1420-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PwzAURS0EEqXwA9gisbAYnr9iZ0QVFKQiFpitxLGLqzRu7USIf49LGBAS03vDOVdXF6FLAjcEQN4mAGAMAykxSKBYHqEZ4RRwBaw6RjMAzjGlUpyis5Q2mZYE2AzR57Eb_K6zRef3o2-LJvp2bVPx4Yf3og89TtsQ8uv7wUZXG5vO0Ymru2Qvfu4cvT3cvy4e8epl-bS4W2HDgAy4dS0reWNVU7PWKEmZUgKgqmktpDCUmYrQJhcGIJI6ZsAx0RArRKlKV1k2R9dT7i6G_WjToLc-Gdt1dW_DmDRRCoByDjyjV3_QTRhjn9t9U0pyUolMkYkyMaQUrdO76Ld1_NQE9GFFPa2ocyl9WFHL7NDJSZnt1zb-Sv5X-gI7dXJZ</recordid><startdate>20160801</startdate><enddate>20160801</enddate><creator>Fel, Leonid G.</creator><creator>Rubinstein, Boris Y.</creator><creator>Ratner, Vadim</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20160801</creationdate><title>Multiple liquid bridges with non-smooth interfaces</title><author>Fel, Leonid G. ; Rubinstein, Boris Y. ; Ratner, Vadim</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c301t-dfd364be8ba3dc8723885009a2a575c23c912b01600172f3c0f35b1e55686f9e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Applications of mathematics</topic><topic>Axisymmetric</topic><topic>Axisymmetric bodies</topic><topic>Boundary conditions</topic><topic>Contact</topic><topic>Engineering</topic><topic>Evolution</topic><topic>Liquid bridges</topic><topic>Liquids</topic><topic>Mathematical analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Theoretical and Applied Mechanics</topic><topic>Triangles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fel, Leonid G.</creatorcontrib><creatorcontrib>Rubinstein, Boris Y.</creatorcontrib><creatorcontrib>Ratner, Vadim</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fel, Leonid G.</au><au>Rubinstein, Boris Y.</au><au>Ratner, Vadim</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multiple liquid bridges with non-smooth interfaces</atitle><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle><stitle>Z. Angew. Math. Phys</stitle><date>2016-08-01</date><risdate>2016</risdate><volume>67</volume><issue>4</issue><spage>1</spage><epage>13</epage><pages>1-13</pages><artnum>107</artnum><issn>0044-2275</issn><eissn>1420-9039</eissn><abstract>We consider a coexistence of two axisymmetric liquid bridges LB
i
and LB
m
of two immiscible liquids
i
and
m
which are immersed in a third liquid (or gas)
e
and trapped between two smooth solid bodies with axisymmetric surfaces
S
1
,
S
2
and free contact lines. Evolution of liquid bridges allows two different configurations of LB
i
and LB
m
with multiple (five or three) interfaces of non-smooth shape. We formulate a variational problem with volume constraints and present its governing equations supplemented by boundary conditions. We find a universal relationship between curvature of the interfaces and discuss the Neumann triangle relations at the singular curve where all liquids meet together.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00033-016-0702-7</doi><tpages>13</tpages></addata></record> |
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| issn | 0044-2275 1420-9039 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Applications of mathematics Axisymmetric Axisymmetric bodies Boundary conditions Contact Engineering Evolution Liquid bridges Liquids Mathematical analysis Mathematical Methods in Physics Theoretical and Applied Mechanics Triangles |
| title | Multiple liquid bridges with non-smooth interfaces |
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